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\author{221330100 WLQ }
\title{插值与拟合习题 }

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\item  叙述并解释三次样条插值函数满足的几个条件。

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\item  求解超定的线性方程组
\begin{eqnarray}
\left\{\begin{array}{rcl}
x+y+z  &=& 10, \\
x+2y+2z  &=& 20, \\
x+3y+5z  &=& 40, \\
x+7y+9z  &=& 90.
\end{array}\right.
\end{eqnarray}

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解答：


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\item  已知某放射性物质衰减的观测数据如表所示。使用这些数据拟合函数
$$y(t) = \beta_1e^{-\lambda_1 t} + \beta_2e^{-\lambda_2 t} $$
中的各个参数 $\beta_1,\lambda_1,\beta_2,\lambda_2$ 的估计值。
\begin{table}[ht!]\centering
\caption{放射性物质浓度的观测数据}\vspace{0.2cm}
\begin{tabular}{|M{1cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|}   \hline 
$t$&0.0&	0.1&	0.2&	0.3&	0.4&	0.5&	0.6 \\ \hline 
$y$&5.8955&	3.5639&	2.5173&	1.9790&	1.8990&	1.3938&	1.1359 \\ \hline\hline
$t$&0.7&	0.8&	0.9&	1.0&	1.1&	1.2&	1.3 \\ \hline
$y$&1.0096&	1.0343&	0.8435&	0.6856&	0.6100&	0.5392&	0.3946 \\ \hline\hline
$t$&1.4&	1.5&	1.6&	1.7&	1.8&	1.9&	2.0 \\ \hline
$y$&0.3903&	0.5474&	0.3459&	0.1730&	0.2211&	0.1704&	0.2636 \\ \hline
\end{tabular}
\end{table}

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解答：


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